<h2>Problem 131</h2>
<div style="color:#666;font-size:80%;">10 November 2006</div><br />
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<p>There are some prime values, <i>p</i>, for which there exists a positive integer, <i>n</i>, such that the expression <i>n</i><img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /> + <i>n</i><img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /><i>p</i> is a perfect cube.</p>
<p>For example, when <i>p</i> = 19, 8<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" /> + 8<img src="" style="display:none;" alt="^(" /><sup>2</sup><img src="" style="display:none;" alt=")" /><img src='images/symbol_times.gif' width='9' height='9' alt='&times;' border='0' style='vertical-align:middle;' />19 = 12<img src="" style="display:none;" alt="^(" /><sup>3</sup><img src="" style="display:none;" alt=")" />.</p>
<p>What is perhaps most surprising is that for each prime with this property the value of <i>n</i> is unique, and there are only four such primes below one-hundred.</p>
<p>How many primes below one million have this remarkable property?</p>

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